Converting Between Units in Litres and Units in Metres Cubed
As well as knowing the relationship between units within sets of units, for volume you also need to know how the two sets of units are related.
You can assume the following:
1 ml = 1 cm3
which leads to:
1 dm3 = 1000 ml 1 litre = 1000 cm3
1 dm3 = 1 litre
1 mm3 = 1 µl
Note: prefixes are not converted directly eg consider milli-
and micro-: millimetres cubed do not convert to millilitres.
Example Conversion
Convert 0.035 litres to millimetres cubed.
1 litre = 1 dm3 = 10-3 m3
1 mm3 = 10-9 m3
1 litre is 10-3 times ie 106 times larger than 1 millimetre cubed.
10-9
Thus: 0.035 l = 0.035 x 1000000 mm3 = 35000 mm3
10-9
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Example Conversion
Convert 75 millimetres cubed to microlitres.
Change millimetre cubed into decimetre cubed and then into litres.
1 mm3 = 10-9 m3
1 dm3 = 10-3 m3
Thus: 1 mm3 = 10-9 / 10-3 = 10-6 dm3
Thus: 1 mm3 = 10-6 litres 1 µl = 10-6 litres
1 dm3 = 10-3 m3
Thus: 1 mm3 = 10-9 / 10-3 = 10-6 dm3
1 mm3 = 1 µl
Thus: 75 mm3 = 75 µl
Thus: 75 mm3 = 75 µl
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1 ml is not exactly 1 cm3.
A litre was defined as the volume of a kilogram of water at 1 atmospheric pressure and 4 °C ie it was supposed to be exactly 1000 cm3.
However, it has since been found that 1 litre actually equals 1000.027 cm3:
the original definition forgot to take into account the AIR DISSOLVED IN THE WATER.
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